# Give the exact value for tan 13pi/3

Give the exact value for tan 13pi/3

it will equal – cot pi/4  which is -1 Its A

Look at the picture.

Undefined Step-by-step explanation: Sec 3/2 = 1/Cos(3/2) = 1/0 = Undefined

Step-by-step explanation: we know that so The angle belong to the II quadrant —-> the function cotangent is negative Remember that therefore

A. The exact value of sec(13π/6) = 2√3/3 B. The exact value of cot(7π/4) = -1 Step-by-step explanation: * Lets study the four quadrants

# First quadrant the measure of all angles is between 0 and π/2   the measure of any angle is α   ∴ All the angles are acute   ∴ All the trigonometry functions of α are positive
# Second quadrant the measure of all angles is between π/2 and π   the measure of any angle is π – α
∴ All the angles are obtuse
∴ The value of sin(π – α) only is positive   sin(π – α) = sin(α)  ⇒ csc(π – α) = cscα
cos(π – α) = -cos(α)   ⇒ sec(π – α) = -sec(α)   tan(π – α) = -tan(α)   ⇒ cot(π – α) = -cot(α) # Third quadrant the measure of all angles is between π and 3π/2
the measure of any angle is π + α   ∴ All the angles are reflex   ∴ The value of tan(π + α) only is positive   sin(π + α) = -sin(α)  ⇒ csc(π + α) = -cscα
cos(π + α) = -cos(α)   ⇒ sec(π + α) = -sec(α)   tan(π + α) = tan(α)   ⇒ cot(π + α) = cot(α)
# Fourth quadrant the measure of all angles is between 3π/2 and 2π     the measure of any angle is 2π – α   ∴ All the angles are reflex
∴ The value of cos(2π – α) only is positive   sin(2π – α) = -sin(α)  ⇒ csc(2π – α) = -cscα
cos(2π – α) = cos(α)   ⇒ sec(2π – α) = sec(α)   tan(2π – α) = -tan(α)   ⇒ cot(2π – α) = -cot(α) * Now lets solve the problem A. The measure of the angle 13π/6 = π/6 + 2π – The means the terminal of the angle made a complete turn (2π) + π/6 ∴ The angle of measure 13π/6 lies in the first quadrant ∴ sec(13π/6) = sec(π/6) ∵ sec(x) = 1/cos(x) ∵ cos(π/6) = √3/2 ∴ sec(π/6) = 2/√3 ⇒ multiply up and down by √3 ∴ sec(π/6) = 2/√3 × √3/√3 = 2√3/3 * The exact value of sec(13π/6) = 2√3/3 B. The measure of the angle 7π/4 = 2π – π/4 – The means the terminal of the angle lies in the fourth quadrant ∴ The angle of measure 7π/4 lies in the fourth quadrant – In the fourth quadrant cos only is positive ∴ cot(2π – α) = -cot(α) ∴ cot(7π/4) = -cot(π/4) ∵ cot(x) = 1/tan(x) ∵ tan(π/4) = 1 ∴ cot(π/4) = 1 ∴ cot(7π/4) = -1 * The exact value of cot(7π/4) = -1